US Special Representative for Afghanistan Reconciliation Zalmay Khalilzad arrived in Islamabad on Sunday to kick off a two-week peace mission that will take him to Afghanistan, Belgium, Germany, Qatar and the United Arab Emirates in efforts to end the long-running Afghan war.

During a visit to the foreign ministry in Islamabad, Khalilzad led his side, which included officials of the US defence and state departments, at delegation-level bilateral consultations with Pakistan. The Pakistan side was led by Additional Secretary Foreign Office Aftab Khokhar and included senior officials of the defence and foreign ministries.

According to an FO statement, the two sides during the talks discussed bilateral ties, the regional law and order situation, the Afghan peace process and other matters of mutual interest.

It quoted Ambassador Khokhar as saying that Pakistan, in accordance with the vision of Prime Minister Imran Khan, will continue to play its role in the Afghan peace process and for regional stability.

He said Pakistan recommends all sides to move towards a political solution in order to end fighting that has been underway in the region for decades

Khalilzad said Pakistan has a "very important" role in the establishment of lasting peace in the region, according to the FO.

In Kabul, the US State Department said Khalilzad would consult with the Afghan government and other Afghans. He is also expected to continue talks with the Taliban in Doha, where the group maintains a political office. At his other stops, Khalilzad will work to build international support for the Afghan peace process.

The talks so far have focused on a timetable for US troop withdrawal from Afghanistan as well as Taliban guarantees that they won't harbour terrorist groups or allow Afghanistan to be used as a staging ground for global terror attacks.

Khalilzad took to Twitter to say he believes the peace process is progressing, even though the last round of talks ended with the two sides at apparent loggerheads over when the US might pull its troops from Afghanistan.

"We've made substantial progress over the last month. On this trip, I want to take that momentum and accelerate the #AfghanPeaceProcess," he wrote.

Khalilzad added that he was optimistic about talks, and called for parties to show "flexibility". He will speak with the Taliban in the Qatari capital Doha, where the two sides have repeatedly met.

The Taliban, however, have refused to negotiate directly with the Kabul government, and the group's leader said on Saturday that they would not call a ceasefire any time soon.

In a rare and defiant message ahead of what would be the seventh round of negotiations, Taliban chief Haibatullah Akhundzada boasted foreign forces in Afghanistan are "condemned to defeat" ─ but said the insurgents would continue talks with the US.

Last year, the Taliban observed a three-day ceasefire over Eid and many Afghans ─ exhausted by decades of war and violence ─ had pinned their hopes on another truce this year.

Afghan President Ashraf Ghani had proposed a nationwide ceasefire at the start of Ramazan early last month, but the Taliban rejected the offer.